Finding the Slope of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

If a line has a slope of 4/3, what does this mean?

Back

A slope of 4/3 means that for every 3 units moved horizontally to the right, the line rises 4 units vertically.

Front

What is the slope of the line represented by the equation y = -5/4x + 2?

Back

The slope of the line is -5/4.

Front

How can you determine if a slope is positive, negative, zero, or undefined?

Back

Examine the rise and run: Positive slope (rise/run > 0), Negative slope (rise/run < 0), Zero slope (rise = 0), Undefined slope (run = 0).

Front

What is the slope of the line if the coordinates of two points are (2, 3) and (2, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.